Gov. Cuomo is flooding the mailboxes of Democratic voters, boasting that he recast New York as the “Progressive Capital of the Country” as he tries to thwart a primary challenge from lefty professor Zephyr Teachout.

Three campaign pieces paid by the New York State Democratic Committee were mailed in recent days promoting Cuomo’s liberal accomplishments to appeal to progressive activists, while ignoring his more centrist or conservative positions.

“From requiring background checks for gun purchases to passing marriage equality and putting us on the road to universal pre-K, Governor Cuomo helped New York reclaim its place as the progressive capital of the country,” one mailer announces.

The mailers also promote Cuomo’s plan to bolster women’s rights and help undocumented residents obtain tuition benefits through the Dream Act.

A state income tax that imposes a higher rate on millionaires and lower rates on middle-class New Yorkers also gets the spotlight, as does a property-tax cap that benefits homeowners.

But the mailers omit the governor’s high-profile policy fight with Mayor de Blasio — a darling of progressives — over higher taxes on the wealthy and doesn’t mention reductions that Cuomo pushed through in corporate and estate taxes.

Four years ago, Cuomo launched his campaign for governor at the Tweed Courthouse and vowed to crack down on “government corruption in Albany.”

But Albany’s ingrained ethics problems were ignored in the campaign literature.

One veteran Democratic Party operative said the mailings were really aimed at propping up his running mate, former Buffalo-area Rep. Kathy Hochul, who is ­unknown in the city and previously staked out some conservative positions.